CLS-21

Centripetal

Uniform circular kinematics.

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GoverningCentripetal

Governing equation

a=v^2/r

$v \in \left[0.5, 80\right]$

where

v: v (m/s)
r: r (m)
a: Centripetal (m/s²)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

a=v^2/r

$v \in \left[0.5, 80\right]$

$v = 0.5$ $a = 0.063$

Along the curve

②

Domain of the variable — blue

v_{\min} = 0.5,\quad v_{\max} = 80

$v \in \left[0.5, 80\right]$

$v = 0.5$ $v = 0.5$

Along the curve

③

Response curve — green

a=v^2/r

$v \in \left[0.5, 80\right]$

$v = 0.5$ $a = 0.063$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}a}{\mathrm{d}v}

$v \in \left[0.5, 80\right]$

$v = 1$ $a^{\prime} = 0.5$

Along the curve

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-21 — Centripetal) is the form associated with Centripetal. Working symbols: $v$ , $r$ $\rightarrow$ $a$ . Uniform circular kinematics. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

a

from

v

r

in Classical mechanics via

a=v^2/r

Uniform circular kinematics. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

v = 12.000\,\mathrm{m/s}

r = 4.000\,\mathrm{m}

, the governing relation

a=v^2/r

yields

a = 36.000\,\mathrm{m/s^{2}}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

v v12 m/sr r4 m

Outputs

Centripetal a36.000 m/s²

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Uniform circular kinematics. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube